Diaschismic family - Revision history

FloraC: Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| "

2026-09-30T17:44:29Z

Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| "

← Older revision		Revision as of 17:44, 30 September 2026
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	Comma list: 126/125, 136/135, 176/175, 196/195, 231/230, 256/255		Comma list: 126/125, 136/135, 176/175, 196/195, 231/230, 256/255

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 2 0 11 31 45 55 5 63 \| 0 1 -2 -8 -12 -15 1 -17 }}		{{Mapping\|legend=2\| 2 0 11 31 45 55 5 63 \| 0 1 -2 -8 -12 -15 1 -17 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 136/135, 256/255		Comma list: 136/135, 256/255

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 2 0 11 5 \| 0 1 -2 1 }}		{{Mapping\|legend=2\| 2 0 11 5 \| 0 1 -2 1 }}
	: mapping generators: ~17/12, ~3		: mapping generators: ~17/12, ~3

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:33:02Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

Show changes

Godtone: /* 13-limit */

2026-09-19T21:45:31Z

13-limit

← Older revision		Revision as of 21:45, 19 September 2026
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	=== 13-limit ===		=== 13-limit ===
	Note that an alternative, simpler mapping for prime 13 exists at -7 gens, as in [[#Shru]]. This mapping is especially valuable when considering shrutar as a no-7's 17-limit temperament (22 & 24, supported by 46, 68f and 70), as the complexity from mapping 7 at +7 gens is one of the motivations for picking a +16 gen mapping for 13. This temperament isn't as accurate, but it is simple, and ~~one could consider a 22- or~~ 24-note ~~half-octave-period~~ MOS ~~scale as relevant~~, with an ~11/8 ~~gen~~.		Note that an alternative, simpler mapping for prime 13 exists at -7 gens, as in [[#Shru]]. This mapping is especially valuable when considering shrutar as a no-7's 17-limit temperament (22 & 24, supported by 46, 68f and 70), as the complexity from mapping 7 at +7 gens is one of the motivations for picking a +16 gen mapping for 13. This temperament isn't as accurate, but it is simple, and makes many [[MOS]]es, specifically 2L 2''n''s for ''n'' up to [[2L 20s\|10]], followed by [[22L 2s]] for the 24-note MOS, with a quarter-tone generator equivalent to ~11/8.

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

Godtone: /* Subgroup extensions */ srutal also uses varda logic

2026-09-19T21:28:03Z

Subgroup extensions: srutal also uses varda logic

← Older revision		Revision as of 21:28, 19 September 2026
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	Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', considered in [[#Subgroup extensions_2\|#Subgroup extensions]]. The [[S-expression]]-based comma list of this temperament is {[[256/255\|S16]], [[289/288\|S17]]}.		Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', considered in [[#Subgroup extensions_2\|#Subgroup extensions]]. The [[S-expression]]-based comma list of this temperament is {[[256/255\|S16]], [[289/288\|S17]]}.

	More generally, one may note that since the fifth of diaschismic is sharp in any good tuning, it is compatible with the logic of [[parapyth]] in making ~13/11 a minor third and ~14/11 a major third, leading to the rank-3 temperament [[varda]], which multiple temps here are rank-2 tunings of, such as 17-limit diaschismic ~~itself~~ (and ~~the~~ obvious ~~extension~~ to prime 23 by mapping it as an augmented fourth aka. tritone~~, na"naa'~~).		More generally, one may note that since the fifth of diaschismic is sharp in any good tuning, it is compatible with the logic of [[parapyth]] in making ~13/11 a minor third and ~14/11 a major third, leading to the rank-3 temperament [[varda]], which multiple temps here are rank-2 tunings of, such as 17-limit diaschismic and srutal (and their obvious extensions to prime 23, na"naa' and srutaloo, both by mapping ~23/16 as an augmented fourth aka. tritone).

	== Septimal diaschismic ==		== Septimal diaschismic ==

Godtone: /* Subgroup extensions */ wording tweak

2026-09-19T21:22:13Z

Subgroup extensions: wording tweak

← Older revision		Revision as of 21:22, 19 September 2026
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	Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', considered in [[#Subgroup extensions_2\|#Subgroup extensions]]. The [[S-expression]]-based comma list of this temperament is {[[256/255\|S16]], [[289/288\|S17]]}.		Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', considered in [[#Subgroup extensions_2\|#Subgroup extensions]]. The [[S-expression]]-based comma list of this temperament is {[[256/255\|S16]], [[289/288\|S17]]}.

	More generally, one may note that since the fifth is sharp in any good tuning, it is compatible with the logic of [[parapyth]] in making ~13/11 a minor third and ~14/11 a major third, leading to the rank-3 temperament [[varda]], which multiple temps here are rank-2 tunings of, such as 17-limit diaschismic itself (and the obvious extension to prime 23 by mapping it as an augmented fourth aka. tritone, na"naa').		More generally, one may note that since the fifth of diaschismic is sharp in any good tuning, it is compatible with the logic of [[parapyth]] in making ~13/11 a minor third and ~14/11 a major third, leading to the rank-3 temperament [[varda]], which multiple temps here are rank-2 tunings of, such as 17-limit diaschismic itself (and the obvious extension to prime 23 by mapping it as an augmented fourth aka. tritone, na"naa').

	== Septimal diaschismic ==		== Septimal diaschismic ==

Godtone: /* Subgroup extensions */ note varda

2026-09-19T21:21:47Z

Subgroup extensions: note varda

← Older revision		Revision as of 21:21, 19 September 2026
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	Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', considered in [[#Subgroup extensions_2\|#Subgroup extensions]]. The [[S-expression]]-based comma list of this temperament is {[[256/255\|S16]], [[289/288\|S17]]}.		Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', considered in [[#Subgroup extensions_2\|#Subgroup extensions]]. The [[S-expression]]-based comma list of this temperament is {[[256/255\|S16]], [[289/288\|S17]]}.

	More generally, one may note that since the fifth is sharp in any good tuning, it is compatible with the logic of [[parapyth]] in making ~13/11 a minor third and ~14/11 a major third, leading to the rank-3 temperament [[varda]], which multiple temps here are rank-2 tunings of.		More generally, one may note that since the fifth is sharp in any good tuning, it is compatible with the logic of [[parapyth]] in making ~13/11 a minor third and ~14/11 a major third, leading to the rank-3 temperament [[varda]], which multiple temps here are rank-2 tunings of, such as 17-limit diaschismic itself (and the obvious extension to prime 23 by mapping it as an augmented fourth aka. tritone, na"naa').

	== Septimal diaschismic ==		== Septimal diaschismic ==

Godtone: /* Subgroup extensions */ note varda

2026-09-19T21:18:47Z

Subgroup extensions: note varda

← Older revision		Revision as of 21:18, 19 September 2026
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	==== Subgroup extensions ====		==== Subgroup extensions ====
	Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', considered in [[#Subgroup extensions_2\|#Subgroup extensions]]. The [[S-expression]]-based comma list of this temperament is {[[256/255\|S16]], [[289/288\|S17]]}.		Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', considered in [[#Subgroup extensions_2\|#Subgroup extensions]]. The [[S-expression]]-based comma list of this temperament is {[[256/255\|S16]], [[289/288\|S17]]}.

			More generally, one may note that since the fifth is sharp in any good tuning, it is compatible with the logic of [[parapyth]] in making ~13/11 a minor third and ~14/11 a major third, leading to the rank-3 temperament [[varda]], which multiple temps here are rank-2 tunings of.

	== Septimal diaschismic ==		== Septimal diaschismic ==

Godtone: /* Shru */ add some details

2026-09-19T21:16:01Z

Shru: add some details

← Older revision		Revision as of 21:16, 19 September 2026
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	== Shru ==		== Shru ==
	Shru tempers out 392/375 and slices the compound semitone into two generators of ~10/7. Its ploidacot is diploid alpha-dicot, the same as shrutar.		Shru tempers out 392/375 and slices the compound semitone into two generators of ~10/7. Its ploidacot is diploid alpha-dicot, the same as shrutar. It can be seen as one way of merging [[parapyth]] with [[diaschismic]] (and hence as a lower-accuracy rank 2 tuning of [[varda]]).

			Note that shru is especially efficient as a no-7's 17-limit temperament, as its 7 is the highest damage, and without it, the other primes can be tuned more accurately.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

Godtone: /* 13-limit */ note hidden intriguing temp

2026-09-19T19:52:44Z

13-limit: note hidden intriguing temp

← Older revision		Revision as of 19:52, 19 September 2026
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	=== 13-limit ===		=== 13-limit ===
			Note that an alternative, simpler mapping for prime 13 exists at -7 gens, as in [[#Shru]]. This mapping is especially valuable when considering shrutar as a no-7's 17-limit temperament (22 & 24, supported by 46, 68f and 70), as the complexity from mapping 7 at +7 gens is one of the motivations for picking a +16 gen mapping for 13. This temperament isn't as accurate, but it is simple, and one could consider a 22- or 24-note half-octave-period MOS scale as relevant, with an ~11/8 gen.

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

FloraC: - echidna (moved to stearnsmic clan as it's a strong extension of it)

2026-09-15T08:12:43Z

- echidna (moved to stearnsmic clan as it's a strong extension of it)

@@ Line 40: / Line 40: @@
 Those all keep the same half-octave period and fifth generator.
-Bidia adds [[3136/3125]], the hemimean comma, with a 1/4-octave period. Shrutar adds [[245/243]] and shru adds [[392/375]], with a quartertone generator. Sruti adds [[19683/19600]] and anguirus adds [[49/48]], with a neutral third or hemitwelfth generator. Those split the original generator in two. Echidna adds [[1728/1715]], the orwellisma, with a ~9/7 generator. Echidnic adds [[686/675]], the senga, with a ~8/7 generator. Those split the original generator in three. Finally, quadrasruta adds [[2401/2400]] and splits the original  generator in four.
+Bidia adds [[3136/3125]], the hemimean comma, with a 1/4-octave period. Shrutar adds [[245/243]] and shru adds [[392/375]], with a quartertone generator. Sruti adds [[19683/19600]] and anguirus adds [[49/48]], with a neutral third or hemitwelfth generator. Those split the original generator in two. Echidna adds [[1728/1715]], the orwellisma, with a ~9/7 generator. Echidnic adds [[686/675]], the senga, with a ~8/7 generator. Those split the original generator in three. Finally, quadrasruta adds [[2401/2400]] and splits the original generator in four.
 ==== Subgroup extensions ====
@@ Line 1,130: / Line 1,132: @@
 Badness (Sintel): 1.10
 == Echidnic ==